ROME (CNN) -- A group representing survivors of sexual abuse by priests named a "Dirty Dozen" list of cardinals it said would be the worst candidates for pope based on their handling of child sex abuse claims.

Their presence on the list is based "on their actions and/or public comment about child sex abuse and cover up in the church," the group said.

The list includes Roman Catholic cardinals from several countries.

SNAP, the Survivors' Network of those Abused by Priests, said as it released the list Wednesday that its accusations were based on media reports, legal filings and victims' statements.

The cardinals named on the list have not yet responded to the move by SNAP.

But when asked about it by CNN, the Rev. Federico Lombardi, spokesman for the Vatican, said: "We believe it is not up to SNAP to decide who comes to conclave and who is chosen ... cardinals can decide themselves without asking SNAP for advice."

Monday, SNAP also called for some of the older cardinals to remove themselves from the meetings held before the election of the new pope, arguing that some have been accused of complicity in protecting priests accused of sexually abusing children.

Cardinals from around the globe have been summoned to Rome to take part in the process of choosing the next pope, after the resignation of Pope Benedict XVI last week.

As of midday, 113 of the 115 cardinals eligible to elect the new pope are in Rome, according to Lombardi. To be eligible to be a part of the group, a cardinal must be under the age of 80.

The two cardinal-electors who are not yet there are Kazimierz Nycz of Warsaw, who should arrive later Wednesday, and Jean-Baptiste Pham Minh Man of Vietnam, who is arriving Thursday.

No date has yet been proposed for the secret election, or conclave, to select the former pontiff's successor.

Silence didn't work

SNAP is intentionally focusing on candidates with a realistic chance of being named pope, its executive director David Clohessy said Wednesday as it released its list.

"The single quickest and most effective step would be for the next pope to clearly discipline, demote, denounce and even defrock cardinals and bishops who are concealing child sex crimes. We think that's the missing piece," he said.

The new pope should order each bishop around the world to hand over "every piece of paper he has on proven, admitted or credibly accused child-molesting clerics to law enforcement," Clohessy said.

Barbara Dorris, victims' outreach director for SNAP, said: "The short answer is we've tried silence, silence didn't work, so we have to speak out. We have to do everything we can to get this information out there."

The Catholic Church has been rocked by a series of child sex abuse scandals in recent years -- and the new pope will be under pressure to deal more effectively with a crisis that has undermined public confidence in the church.

Media leaks concern

A news conference scheduled by American cardinals for Wednesday, following press briefings on Monday and Tuesday, was canceled at short notice without explanation.

Asked if the Vatican had told the American cardinals to stop their daily press briefings, Vatican spokesman the Rev. Thomas Rosica suggested that what was discussed in the general congregations was not meant to be publicized.

"It's not up to Father Lombardi or myself to tell them what to do," he said. "It could be that among themselves they realized that there are different ways and different methods of getting things out."

"Concern was expressed in the General Congregation about leaks of confidential proceedings reported in Italian newspapers," Sister Mary Ann Walsh, director of media relations for the U.S. Conference of Catholic Bishops, said via e-mail.

"As a precaution, the cardinals have agreed not to do interviews."

In total, 153 cardinals gathered Wednesday at the Vatican for a third day of meetings, known as general congregations, before they set the timetable for the election.

The cardinals spoke about new evangelization, restructuring of the church hierarchy, or curia, and the need for good governance of the church, Lombardi said.

A five-minute limit has been imposed on cardinals speaking at the meetings, although the microphone is not being switched off if they run over the time allowed.

The cardinals have decided to meet twice Thursday, in the morning and afternoon, in order to "intensify the rhythm of work," Lombardi said.

An elevated floor is being put in place to protect the original mosaic tiling, said Lombardi, on which seats will be placed for the cardinals.

The Sistine Chapel and its ornate ceiling by Michelangelo are normally a must-see for tourists in Rome, but it was closed to the public beginning Tuesday afternoon to allow for preparations to take place.

CNN's Richard Allen Greene and Hada Messia reported from Rome, and Laura Smith-Spark reported and wrote in London.